1. Thermodynamics and Statistical Physics
Lecture 5
Entropy
Second law of thermodynamics
Variable dependences of thermodynamic relationships
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PHY 341/641 Spring Lecture 5

2. Note that dS is an “exact differential” dQ is not.
Entropy for a reversible process (quasi-static via continuous changes in the variables):
Note that dS is an “exact differential” dQ is not.
Carnot cycle.
7/24/2019
PHY 341/641 Spring Lecture 5

3. Square cycle:
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PHY 341/641 Spring Lecture 5

4. Second law of thermodynamics
Kelvin-Planck: It is impossible to construct an engine which, operation in a cycle, will produce no other effect than the extraction of energy from a reservoir and the performance of an equivalent amount of work.
Clausius: No process is possible whose sole result is cooling a colder body and heating a hotter body.
Gould-Tobochnik:There exists an additive function of state known as the entropy S that can never decrease in an isolated system.
7/24/2019
PHY 341/641 Spring Lecture 5

5. Comment on “quasi-static” restrictions
Consider the free expansion of an isolated ideal gas, initially in left chamber at V1 with vacuum in right chamber and finally occupying full volume V2.
In order to use the laws of thermodynamics, we must envision a quasi-static process that accomplishes the free expansion
7/24/2019
PHY 341/641 Spring Lecture 5

6. Variables and functions:
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PHY 341/641 Spring Lecture 5

7. Assume N constant --
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PHY 341/641 Spring Lecture 5

8. Further relations:
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PHY 341/641 Spring Lecture 5

9. Mathematical transformations for continuous functions of several variables & Legendre transforms:
7/24/2019
PHY 341/641 Spring Lecture 5

10. Mathematical transformations for continuous functions of several variables & Legendre transforms continued:
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PHY 341/641 Spring Lecture 5

11. For thermodynamic functions:
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PHY 341/641 Spring Lecture 5

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PHY 341/641 Spring Lecture 5

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PHY 341/641 Spring Lecture 5